Redundant systems are designed using multiple copies of the same resource (e.g., a logic network or a software module) in order to increase system dependability. Design diversity has long been used to protect redundant systems against common-mode failures. The conventional notion of diversity relies on "independent" generation of "different" implementations of the same logic function. In a recent paper, we presented a metric to quantify diversity among several designs. The problem of calculating the diversity metric is NP-complete (i.e., can be of exponential complexity). In this paper, we present efficient techniques to estimate the value of the design diversity metric. For datapath designs, we have formulated very fast techniques to calculate the value of the metric by taking advantage of the regularity in the datapath structures. For general combinational logic circuits, we present an adaptive Monte-Carlo simulation technique for estimating accurate bounds on the value of the metric.